Rendering an animation then saving it as a video is black
The box called Sky has a Background shader. This shader is only meant for the world, and it is ignored on anything else. While the box is hidden from the vireport, it is still enabled during render, and it occludes the background light coming from the world. If I give it an Emission shader, I get this.
  

If I disable it altogether, I get this.
  

The sun lamp is a special type of light, that basically only gives a direction and a strength, and act like it is always outside the scene, regardless of where you actually put it, so even if it's located inside the Sky box, the box occludes its light. Take a look at Lamps in the Blender online manual.